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Full text of "Field book"



MADE IN as A. 



Our Leather Bound Engineers Note Books 
are carried in the following rulings: 



No. 380 LEVEL BOOK. 



No. 382 FIELD BOOK. 



No. 384 MINING TRANSIT 
BOOK. 

No. 385 FIELD BOOK. 



Left and Right Hand Page 
the same as Left Hand Page 
of this Book. 

Left Hand Page as in this 
Book, Right Hand Page 4x4 
to the inch. Center Line Red. 

Left Hand Page as in this 
Book, Right Hand Page 8x8 
to the inch. Center Line Red. 

Left Hand Page as in this 
Book, Right Hand Page 8 ver- 
tical and 4 horizontal lines to 
the inch, Center Line Red. 



We also carry the Note Books listed above, 
bound in extra strong Fabri-Hide (otherwise 
the same quality of book,) which can be fur- 
nished at a somewhat lower price. 

In ordering Fabri-Hide covered books, add 
the letter *'F'' to catalog number. 

THE FREDERICK POST CO. 

ENGINEERING and DRAFTING SUPPLIES 
P. O. Box 803 CHICAGO 



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<^ 


>r: 


} 


c 


V 


'£ 


> 














> 


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"i3 




















< 


?^ 


^ 
f ^ 


^ 


> 


c 


7 , 


/ 


^ 


t:> 


fS 


/< 


^. 


^ 


^ 




































/ 


^/ 


> 


'c 


^ 




<^ 


/ 




2 


^ 


^ 


<5 








1 
































/ 


t^ 


^ 




<: 


r^ 


/ 


i 


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? 










































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V 


a 


i 


J 




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. 
































; 


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"^ 




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^> 


^^ 


s 


f 


^ 


^. 


a< 


1^ 















^f7«^ 


>^''7S 






/^^' 


'-^^r 


/z^<^ 












f.Z^ 










7.0S' 


/f^^? 


^/■43 


-s-^r 






./// 


z-?-;^^ 










rzo 


^-tf^r 










7X?<^ 


f,^^ 




1 




7J^ 


f.B^" 










zc^<:> 





^/ ^.r 


/^^y 






¥JS 


/^54 










7^. 


>?^^ 










'^fS" 


9:7<^ 


///30 


yi^v 






4^0^ 


M^o 










^^ 


f^^\ 










C96" 


^^aA 




^ /TlOr- 


r ^vy 


/^^fo 






S-f^ 


JP^^^ 






Sys^ 


/J' OS 








^/ / " 


\ 41 




1 




7f^i f./ipi 


fj _ 


j^/r£ 








' ,»' ' 










Zfo 




1 






17^cJ ^^c^i 


" 


J^Sd'i^' 






1 
/ 


/ZJKI 










ys2 


/.^^l 








f/^ 


97^% 


k. 








1 


mA 



^y/jra^^ 



\m^ 



%. 






. h^ \ .■ 



■^S. 









^k. 



A^AW^i 



K 



Jt',i<r-f 



'TS-O 



^ 



^ 



C^IC 






^r 



~l. 



y^^ti 






/- 



^l>^ 



2- 



j^/9'Af/k^ey^i^S 5\^^ 



l^r'-^- \ /^^^, /^^ 



m- 



^•^' |/K ^y 



:^Sj^M 



/^/ry. 4^2W 



u^r^ 7j^ , 9.4^ 



r^^^ 



^\//.si%L 



t^^\l5.i^ 









-^^ 



_^^/^ 






/^'/^ 





; 


_J^.76 


■ 1 


^ ^ z^ 


_i;-i5 J 






H 


fr.^ v 




:^'^7 , 


i : 




, . ^^.^;^ 


1 1 






p^z 1 




i 

i 




: 'f 


^■6^ ^ 




! 






/^ /' ^ i 










' yj^ 










; 7.^5 












[.7>^ii 




jr^/^ 


3./;:^ 


16 U 








//^O'V 






.'- . 


^.^^ 










^'fO 


M^ 












1 



•f ^t^f ff I trr ^ 




mSx 






J0^ 



-t - -1 — 


^t^4^ 


1 












' 








^ /<' 


1>>^. 


/r^K 






























:; 







A 



r 



c'y^ 



r>^: 



J '^^kj^ r^ 



<l.^J^^ziLM. 



i 



•T'-i 



^ 



^/^ 



r^ /- 



^ (<'^ 






"nZilSi-tB 











1 

i 




i^T' 










1 


- 


~ T 




-> 


K/^ 




7* 






vV ' ^-^ 














-^ : 






' ■ 1 

■ ' ^ ' i 

1 - 1 ! 






. Oj 


r- \ 


^p^ 










___..^j._:. 


f ■ - ■ I 






i 
j 


^^ 




f 




1 


























•-. 


i 








; 


































1 










! 










1 ^! 


! 

1 




i, 
J 






1 4 






1 1 

J 


1 






It 


^ 


1 






1 



IMPROVED TABLES 

AND 

INFORMATION 





HORIZONTAL STADIA 


CORRECTIONS 




2''— 00' 


— 0.1 




21^—00' — 


12.8 




33°— 00' 


— 29.7 


3°— 00' 


— 0.3 




21°— 30' — 


13.4 




33°— 15' 


— 30.1 


4^—00' 


— 0.5 




22°— 00' — 


14.0 




33°— 30' 


— 30.5 


5^—00' 


— 0.8 




22°— 30' — 


14.7 




33°— 45' 


— 30.9 


6"— 00' 


— 1.1 




23°— 00' — 


15.3 




34°— 00' 


— 31.3 


7"^— 00' 


— 1.5 




23°— 30' — 


15.9 




34°— 15' 


— 31.7 


8^—00' 


— 1.9 




24°— 00' — 


16.5 




34°— 30' 


— 32.1 


9^—00' 


— 2.5 




24°— 30' — 


17.2 




34°* 45' 


— 32.5 


10^—00' 


— 3.0 




25°— 00' — 


17.9 




35°— 00' 


— 32.9 


10"— 30' 


— 3.3 




25°— 30' — 


18.6 




35°— 15' 


— 33.3 


11'— 00' 


— 3.6 




26°— 00' — 


19.2 




S5°— 30' 


— 33.7 


11^—30' 


— 4.0 




26°— 30' — 


19.9 




35°— 45' 


— 34.1 


12^—00' 


— 4,3 




27°— 00' — 


20.6 




36°— 00' 


— 34.6 


12'— 30' 


— 4.7 




27^—30' — 


21.3 




36°— 15' 


— 35.0 


13^-00' 


— 5.1 




28°— 00' — 


22.0 




36°— 30' 


— 35.4 


13^-30' 


— 5.5 




28°— 30' — 


22.S 




36° 45' 


— 35.8 


14^-00' 


— 5.9 




29°— 00' — 


23.5 




37°— 00' 


— 36.2 


14^—30' 


— 6.3 




29°— 30' — 


24.3 




37°— 15' 


— 36.6 


15°— 00' 


— 6.7 




30°— 00' — 


25.0 




37°— 30' 


— 37.1 


15°— 30' 


— 7.2 




30°— 15' — 


25.4 




37° 45' 


— 37.5 


16°— 00' 


— 7.6 




30°_30' — 


25.8 




38°— 00' 


— 37.9 


16°— 30' 


— 8.1 




30^—45' — 


26.2 




38°— 15' 


— 38.3 


17°— 00' 


— 8.5 




31°_00' — 


26.5 




38°— 30' 


— SS.7 


17°— 30' 


— 9.0 




SV—Id — 


26.9 




38°— 45' 


— 39.1 


18°— 00' 


— 9.5 




31°— 30' — 


27.3 




39°— 00' 


— 39.6 


18°— 30' 


— 10.1 




31°— 45' — 


27,7 




39°— 15' 


— 40.0 


19°— 00' 


— 10.6 




32=_00' — 


28.1 




39°— 30' 


— 40.5 


19°— 30' 


— 11.2 




32^—15' — 


28.5 








20°— 00' 


— 11.7 




32°— 30' — 


28.9 








20°— 30' 


— 12.3 




32°— 45' — 


29.3 









Chains 


to Feet 


1 


66 


2 


132 


3 


198 


4 


264 


5 


..... 330 


6 


396 


7 


.... 462 


8 


.... 528 


9 


.... 594 


10 


660 



Feet to 


Chains 


100 .. 


. 1,515 


200 . 


.. 3.030 


300 .. 


. 4.545 


400 .. 


. 6.060 


500 .. 


. 7.575 


600 .. 


. 9.090 


700 .. 


. 10.606 


800 .. 


. 12.121 ^ 


900 .. 


. 13.636 


1,000 .. 


. 15.151 



DIRECTIONS FOR USE OF TABLES 



TABLE No. 1. 

Distance of slope stake from side or shoulder 
stake for any width roadway, slope 1 ^ to 1 . 
If ground is nearly level, the cut or fill at side 
stake is located by the double entry method in 
left column and top row. The number in body 
of table in same row and column gives distance 
from side stake to slope stake. If ground is not 
level estimate the difference in elevation between 
the side stake and slope stake, lower target by this 
amount if cut, elevate if fill. Add this amount 
to cut or fill and find distance in table. Set up 
rod at this point, and line of sight should cut 
target If it does not make the slight adjustment 
necessary. 

TABLE No. 9. 

To find Tangent and External for curve of 
any other degree, divide by degree of curve and 
add correction found in column of corrections. 

Degree of curve with a given I may be found 
by dividing tangent, (or external), opposite I by 
given tangent, (or external). 

The distance from a point on the tangent to 
the curve is very nearly the square of the tangent 
lenth divided by twice the radius. 





"^ 


V 


^ 




^ 


<i 


\ 




N . 


^\ 


4 


\ 




8>\ 






' 




f^^ 1 


/ 













'- 1 


A! 



1 ^^ 



ZA: 



ilMOP 
R 



Table II 
TRIGONOMETRIC FORMULiE. 
ZB= ZP0N=: /OPL 
t OB = c = 1 



a a 

sin A = — = -^ s= a = coe B = LP 
c 1 

b b 

cos A = = -— - = b = sin B = OL 

c 1 

^ . a MQ 

tan A = = — 

^^ b OM 



MQ 

1 



= MQ = oot B « MQ 



cot A = 

08C A « 

vers A = 
covers A 



NT 
ON 

OQ 

OM 
OT 
ON '' 
LM 



NT 



1 
OQ 



1 

OT 
1 



= NT = tanB = NT 
= OQ = cac B = OQ 
= OT = sec B = OT 



= LM = covers B # 



OP 
OP — LP 
OP 



= OP — LP = vers B 



exsec A = PQ = coexsec B 
coexsec A == PT = exsec B 



sin H A = 



^' 



— CosA 



cos J^ A 



-I' 



+Cos A 



sin 2A =: 2 sin A cos A 
Law of Lines 



cos 2 A = cos' A — sin' A 
sin B sin O 



a "" B "^ C 

Law of Cosines c' = a' 4- b=* — 2 ab cos C 

T trr . a+^ t an H (A-f B) 

Law of Tangents r- = ■- r-:-r-r ^ 

a — b tan Ji (A — B) 



Table II — Continued 
TRIGONOMETRIC FORMULAE (continued) 
In any triangle: 

Given a, b, C; to find c, B, A. 

Use Law of Lines. 
Given A B, c; to find a, b, C. 

Use Law of Lines. 
Given a, b, c; to find A, B, C. 

a + b + c I (s — a) (s — b) (s — c) 



Let 



I (s — a) (s — 



= r 



cos 



H*-^|^ 



a) 



tan H A = 
tan HB = 



8 — a 

r 



tan HG = 



8 — c 
Area of a triangle : 
Area = }^ ab Sin C 



Area = \/s (s — a) (s — b) (s — c) 

PRISMOIDAL FORMULA. 

Vol. =4-(B + b-h4M) 
o 

h = altitude; b, B = bases; M = midsection 



Table III 

INCHES AND FRACTIONS OF AN INCH IN DECIMALS OF A 

FOOT 








1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 




A 


.0052 


.0885 


.1719 


.2552 


.3385 


.4219 


.5052 


.5885 


.6719 


.7552 


.8385 


.9219 


A 


Vs 


.0104 


.0938 


.1771 


.2604 


.3438 


.4271 


.5104 


.5938 


.6771 


.7604 


.8438 


.9271 


Vs 


A 


.0156 


.0990 


.1823 


.2656 


.3490 


.4323 


.5156 


.5990 


.6823 


.7656 


.8490 


.9323 


A 


yi 


.0208 


.1042 


.1875 


.2708 


.3542 


.4375 


.5208 


.6042 


.6875 


7708 


.8542 


9375 


}4 


ti 


.0260 


.1094 


.1927 


.2760 


.3594 


.4427 


.5260 


.6094 


.6927 


.7760 


.8594 


9427 


A 


.0313 


.1146 


.1979 


.2813 


.3646 


.4479 


.5313 


.6146 


.6979 


.7813 


.8646 


.9479 


Vs 


A 


.0365 


.1198 


.2031 


.2865 


.3698 


.4531 


.5365 


.6198 


.7031 


.7865 


.8698 


.9531 


A 


H 


.0417 


.1250 


.2083 


.2917 


.3750 


.4583 


.5417 


.6250 


.7083 


.7917 


.8750 


.9583 


'A 


A 


.0469 


.1302 


.2135 


.2969 


.3803 


.4635 


.5469 


.6302 


.7135 


.7969 


.8802 


.9635 


A 


Vs 


.0521 


.1354 


.2188 


.3021 


.3854 


.4688 


.5521 


.6354 


.7188 


.8021 


.8854 


.9688 


H 


H 


.0573 


1406 


.2240 


.3073 


.3906 


.4740 


.5573 


.6406 


.7240 


.8073 


.8906 


.9740 


H 


H 


.0625 


.1458 


.2292 


.3125 


.3958 


.4792 


.5625 


.6458 


.7292 


.8125 


.8958 


.9792 


M 


4 


.0677 


.1510 


.2344 


.3177 


.4010 


.4844 


.5677 


.6510 


.7344 


.8177 


.9010 


.9844 


H 


Vs 


.0729 


.1563 


.2396 


.3229 


.4063 


.4896 


.5729 


.6563 


.7396 


.8229 


.9063 


.9896 


Vs 


H 


0781 


.1615 


.2448 


.3281 


.4115 


.4948 


.5781 


.6615 


7448.8281 


.9115 


.9948 


H 


1 


.0833 


.1667 


.2500 


.3333 


.4167 


.5000 


.5833 


.6667 


.7500.8333 


.9167 


1.000 


1 







1 


2 


3 


4 


5 


6 


7 


8 9 


10 


11 









Table IV 






USEFUL RELATIONa 


Lineal feet 


X. 00019 


= miles 


Lineal yards 


X.0006 


= miles 


Square inches X. 007 


= square feet 


Square feet 


X.lll 


= square yards 


Square yards 


X. 0002067 = acres 


Acres 


X4840 


= square yards 


Cubic inches 


X. 00058 


= cubic feet 


Cubic feet 


X. 03704 


= cubic yards 


Links 


X.22 


= yards 


Links 


X.66 


= feet 


Feet 


X1.5 


= links 



360° = 21600' = 1296000" 
Radius = arc of 57.2957790° 
Arc of 1° (radius = 1) = .017453292 
Arc of 1' (radius = 1) = .000290888 
Arc of V (radius = 1) = .000004848 

X = 3.141592654 ^ — = 0.564190 



3| 6 



4 1 

— = 1.128379167 — , = 0.101321184 

t: x^ 



JL = 0.785398163 ^ ! — ' = 1.240700982 

4 ^ X 

— = 0.523698776 t^' = 9.869604401 
6 

— = 0.523598776 \/x'= 1.772453851 

— = 4.188790205 — = 0.3183099 

3 X 

Curvature of Earth's surface = about 0.7 feet in 1 mile 

Curvature in feet = 0.667 (Dist. in miles)* 

Difference between arc and chord length, 0.05 feet in 113^ miles 






Probable error of a single observation = 0.6754 

Error in chaining of 0.01 feet in 100 feet: 
Due to — 

1. Length of tape error of 0.01 feet 

2. Alignment. One end 1.4 feet out of line 

3. Sag of tape at centre of 0.61 feet. 

4. Temperature difference of 15° 
6. Difference of pull of 15 lbs. 

STADIA REDUCTION FORMULiE. 
Horizontal Distance = R — R sin' a+C cos a 
Vertical Distance = R 3^ sin 2 a 4- C sin a 

__ distance from Object glass to cross hairs 

~ distance between cross hairs 

C = distance from Object glass to cross hairs 4- distance from Object 

glass to center of instrument. 
a = angle of elevation for mid Reading 




Table V 
CURVE FORMULAE FOR SIMPLE CURVES 
Compiled by J. Calvin Locke, C.E, 
(1) c = \/ 2R^ (2) c = V^JTh^ 

(3) c = V 2R(R — \/( R-j-b) (R — b) = \/2R(R — \/R'— b^ 

(4) c = 2\/m (2R — m) 

(5) c = 2R sin H I (6) c = 2T cos H I 
(7) e = R exsec H I 



(8) e = R tan H I tan J^ I 
(10) b = \/a(2R — a) 



(9) e = T tan }4 I 



"■'-^'("^)0-^)-^| 



(12) b 
(14) R = 



RsinI 
a^ + b' 



2R 

(13) b = a cot H I 

(15) R = 



2a 



2m 



4R» 

_ c'4-4m' 

8m 



(16) d == Vr (2R— V(2R + c) (2R — c) = \/r(2R — \/4R^ — cO 

(17) d = \/2R^ (18) d = 2R sin 1^ I (19) m = 



2R 



(20) ™ = Rt^(r+-|-)(r-A) = Rt^R.— ^ 

(21) m = R vers H I (22) m = R sin 3^ I tan 3^ I (23) m = H c tan 3^ I 
(24) a = -^— (25) a = R — V(R-f-b) (R — b) = R — VR' — b> 

(20) a = 2 R (sin^ 3^ I)^ (27) a = R vers I (28) a = R sin I tan 3^ 
(29) a = b tan 3^ I (30) a = T sin I (31) T = R tan 3^ I 



(32) I = -^X 57. 295780 



(33) R = —X 57. 295780 



(34) L = IRXO.01745329 (35) L = 



8d — c 



(30) Area So^. = 



LR 



- R^ Sin I 

2 



LR — Rb 



Table VI 
SINES, COSINES, TANGENTS, COTANGENTS 



bX) 


sin 


tan 


sin 


tan 


sin 


tan 


sin 


tan 


sin 


tan 


sin 


tan 


hO 




0' 


0' 


lO' 


10' 


20' 


20' 


30' 


30' 


40' 


40' 


50' 


50' 








0000 


0000 


0029 


0029 


0058 


0058 


0087 


0087 


0116 


0116 


0145 


0145 


S9 


1 


175 


0175 


0204 


0204 


0233 


0233 


0262 


262 


291 


291 


320 


320 


S8 


2 


349 


349 


378 


378 


407 


407 


436 


437 


465 


466 


494 


495 


87 


3 


523 


524 


552 


553 


581 


582 


610 


612 


640 


641 


669 


670 


86 


4 


698 


699 


727 


729 


756 


758 


785 


787 


814 


816 


843 


864 


85 


6 


872 


875 


901 


904 


929 


934 


958 


963 


987 


992 


1016 


1022 


84 


6 


1045 


1051 


1074 


1080 


1103 


1110 


1132 


1139 


1161 


1169 


190 


198 


83 


7 


219 


228 


248 


257 


279 


287 


305 


317 


334 


346 


363 


376 


82 


8 


392 


405 


421 


435 


449 


465 


478 


495 


507 


524 


536 


554 


81 


9 


564 


584 


593 


614 


622 


644 


650 


673 


679 


703 


708 


733 


80 


10 


736 


763 


765 


793 


794 


823 


822 


853 


851 


883 


880 


914 


79 


11 


908 


944 


937 


974 


965 


2004 


994 


2035 


2022 


2065 


2051 


2095 


78 


12 


2079 


2126 


2108 


2156 


2136 


186 


2164 


217 


193 


247 


221 


278 


77 


13 


250 


309 


278 


339 


306 


370 


334 


401 


363 


432 


391 


462 


76 


14 


419 


493 


447 


524 


476 


555 


504 


586 


532 


617 


560 


648 


75 


15 


588 


679 


616 


711 


644 


742 


672 


773 


700 


805 


728 


836 


74 


16 


756 


867 


784 


899 


812 


931 


840 


962 


868 


994 


896 


3026 


73 


37 


924 


3057 


952 


3089 


939 


3121 


3007 


3153 


3035 


3185 


3062 


217 


72 


IS 


3090 


249 


3118 


281 


3145 


314 


173 


346 


201 


378 


228 


411 


71 


19 


256 


443 


283 


476 


311 


508 


338 


541 


365 


574 


393 


607 


70 


20 


420 


640 


448 


673 


475 


706 


502 


739 


529 


772 


557 


805 


69 


21 


584 


839 


611 


872 


638 


906 


665 


939 


692 


973 


719 


4006 


68 


22 


746 


4040 


773 


4074 


800 


4108 


827 


4142 


854 


4176 


881 


210 


67 


23 


907 


245 


934 


279 


961 


314 


987 


348 


4014 


383 


4041 


417 


66 


24 


4067 


452 


4094 


487 


4120 


522 


4147 


557 


173 


592 


200 


628 


65 


25 


226 


663 


253 


699 


279 


734 


305 


770 


331 


806 


358 


841 


64 


26 


384 


877 


410 


913 


436 


950 


4462 


986 


488 


5022 


514 


6059 


63 


27 


540 


5095 


566 


5132 


592 


5169 


617 


5206 


643 


243 


669 


280 


62 


28 


695 


317 


720 


354 


746 


392 


772 


430 


797 


467 


823 


505 


61 


29 


848 


643 


874 


581 


899 


619 


924 


658 


950 


696 


975 


735 


60 


30 


5000 


774 


5025 


5812 


5050 


851 


5075 


890 


5100 


930 


5125 


969 


59 


31 


150 


6009 


175 


6048 


200 


6088 


225 


6128 


250 


6168 


275 


6208 


58 


32 


299 


249 


324 


289 


3i8 


330 


5373 


371 


398 


412 


422 


453 


57 


33 


446 


494 


471 


536 


495 


577 


519 


619 


544 


661 


568 


703 


56 


34 


592 


745 


616 


787 


640 


830 


664 


873 


688 


916 


712 


959 


55 


35 


736 


7002 


760 


7046 


783 


7089 


807 


7133 


831 


7177 


854 


7221 


54 


36 


878 


265 


901 


310 


925 


355 


948 


400 


972 


445 


995 


490 


53 


37 


6018 


536 


6041 


581 


6065 


627 


6088 


673 


6111 


720 


6134 


766 


52 


38 


157 


813 


180 


860 


202 


907 


225 


954 


248 


8002 


271 


8050 


51 


39 


293 


8098 


316 


8146 


338 


8195 


361 


8243 


383 


292 


406 


342 


50 


49 


428 


391 


450 


441 


472 


491 


494 


641 


617 


691 


639 


642 


49 


41 


561 


693 


583 


744 


604 


796 


626 


847 


648 


899 


670 


952 


48 


42 


691 


9004 


713 


9057 


734 


9110 


756 


9163 


777 


9217 


799 


9271 


47 


43 


820 


325 


841 


380 


862 


435 


884 


490 


905 


545 


926 


601 


46 


44 


947 


657 


967 


713 


988 


770 


17009 


827 


7030 


884 


7050 


942 


45 


45 


7071 


1.0000 


7092 


1.0058 


7112 


1.0117 


133 


1.0176 


153 


1.0235 


173 


1.0295 


44 


bD 


eo' 


60' 


50' 


5^ 


40' 


40^ 


30' 


30' 


20' 


20 


10' 


10' 


• 
bO 


•2. 


cos 


cot 


COS 


cot 


cos 


cot 


cos 


cot 1 cos 


cot 


cos 


cot 


9i 

J3l 



Table VI (continued) 
SINES, COSINES, TANGENTS, COTANGENTS (continued) 



t£ 


sin 


tan 


sin 


tan 


sin 


tan 


sin 


tan 


sin tan 


sin 


tan 


th 


4> 


0' 


C 


10' 


IC 


20' 


20' 


30' 


30' 


40' 4^ 


50' 


50' 


^ 


46 


7193 


1.0355 


7214 


[ i.04ie 


»7234 


1.0477 


7254 


1.0533 


7274 1.0599 


7294 


1.0661 


43 


47 


314 


.0724 


332 


.078C 


) 353 


,0850 


373 


.0913 


392 


.0977 


412 


.1041 


42 


48 


431 


.1106 


451 


.1171 


470 


.1237 


490 


.1303 


509 


.1369 


528 


.1436 


41 


49 


647 


.1504 


666 


.1571 


585 


.1640 


604 


.1708 


623 


.1778 


642 


.1847 


40 


50 


660 


1.1918 


7679 


1.1985 


7698 


1.2059 


7716 


1.2131 


7735 


1.2203 


7753 


1.2276 


39 


51 


771 


.2349 


790 


.2423 


808 


.2497 


826 


.2572 


844 


.2647 


862 


.2723 


38 


52 


880 


.2799 


898 


.2876 


916 


.2954 


934 


.3032 


951 


.3111 


969 


.3190 


37 


53 


986 


.3270 


8004 


.3351 


8021 


.3452 


8039 


.3514 


8056 


.3597 


8073 


.3680 


36 


54 


8090 


.3764 


107 


.3848 


124 


.3934 


141 


.4019 


158 


.4106 


175 


.4193 


35 


55 


192 


.4281 


208 


.4370 


225 


.4460 


241 


.4550 


258 


.4641 


274 


.4733 


34 


56 


290 


.4826 


307 


.4919 


323 


.5013 


339 


.5108 


355 


.5204 


371 


.5301 


33 


57 


387 


.5399 


403 


.5497 


418 


.6597 


434 


.5697 


450 


.6798 


465 


.5900 


32 


58 


480 


.6003 


496 


.6107 


611 


.6212 


526 


.6319 


642 


.6426 


657 


.6534 


31 


59 


672 


.6643 


687 


.6753 


601 


.6864 


616 


.6977 


631 


.7090 


646 


.7205 


30 


60 


660 


1.7321 


8675 


1.7437 


8689 


1.7556 


8704 


1.7675 


8718 


1.7797 


8732 


1.7917 


29 


61 


746 


.8040 


760 


.8165 


774 


.8291 


788 


.8418 


802 


.8546 


816 


.8676 


28 


62 


829 


.8807 


843 


.8940 


857 


.9074 


870 


.9210 


884 


.9347 


897 


.9486 


27 


63 


910 


.9626 


923 


.9768 


936 


.9912 


949 


2.0057 


962 


2.0204 


975 


2.0353 


26 


64 


988 


2.0503 


9001 


2.0655 


9013 


2.0809 


9026 


.0965 


9038 


.1123 


9051 


.1283 


25 


65 


9063 


.1445 


075 


.1609 


088 


.1775 


100 


.1943 


112 


.2113 


124 


.2286 


24 


66 


135 


.2460 


147 


.2637 


159 


.2817 


171 


.2998 


182 


.3183 


194 


.3369 


23 


67 


205 


.3559 


216 


.3750 


228 


.3945 


239 


.4142 


250 


.4342 


261 


.4545 


22 


68 


272 


.4751 


283 


.4960 


293 


.5172 


304 


.6386 


315 


.6605 


325 


.5826 


21 


69 


336 


.6051 


346 


.6279 


356 


.6511 


367 


.6746 


377 


.6985 


387 


.7228 


20 


70 


397 


27475 


9407 


2.7725 


9417 


2. 7980 


9426 


2.8239 


9436 


2.8502 


9446 


2.8770 


19 


71 


455 


.9042 


465 


.9319 


474 


.9600 


483 


.9887 


492 


3.0178 


502 


3.0475 


18 


72 


511 


3.0777 


520 


3.1084 


528 


3.1397 


537 


3.1716 


646 


.2041 


555 


.2371 


17 


73 


563 


.2709 


572 


.3052 


580 


.3402 


588 


.3759 


696 


.4124 


605 


.4495 


16 


74 


613 


.4874 


621 


.5261 


628 


.5656 


636 


.6059 


644 


.6470 


652 


.6891 


15 


75 


659 


7321 


667 


.7760 


674 


.8208 


681 


.8657 


689 


.9136 


696 


.9617 


14 


76 


703 


4.0108 


710 


4.0611 


717 


4.1126 


724 


4.1653 


730 


4.2193 


737 


4.2747 


13 


77 


744 


.3315 


750 


.3897 


757 


.4494 


763 


.5107 


769 


.5736 


775 


.6382 


12 


78 


781 


.7046 


787 


.7729 


793 


.8430 


799 


.9152 


805 


.9894 


811 


5.0658 


11 


79 


816 


.1446 


822 


5.2257 


827 


5. 3093 


833 


6.3955 


838 


5.4845 


843 


.5764 


10 


80 


9848 


5.6713 


9853 


5.7694 


9858 


5. 8708 


9863 


6.9758 


9868 


6.0844 


9872 


6.1970 


9 


81 


877 


6.3138 


881 


6 4348 


886 


6.5606 


890 


6.6912 


894 


.8269 


899 


.9682 


8 


82 


903 


7.1154 


907 


7.2687 


911 


7.4287 


914 


7.5958 


918 


7.7704 


922 


7.9530 


7 


83 


925 


8.1443 


929 


8.3450 


932 


8.5555 


936 


8.7769 


939 


9.0098 


942 


9.2553 


6 


84 


945 


9.5144 


948 


9.7882 


951 


10.078 


954 


10.385 


957 


10.711 


959 


11.059 


5 


85 


962 


11.430 


964 


11.826 


967 


12.250 


969 


12.706 


971 


13.197 


974 


13.727 


4 


86 


976 


14.300 


978 


14.924 


980 


15.605 


981 


16 '350 


983 17.169 


985 


18.075 


3 


87 


986 


19.081 


988 


20.206 


989 


21.470 


990 


22.903 


992 24542 


993 


26.432 


2 


88 


994 28.636 


9995 


31.242 


9996j 


34.368 


997 


38.189 


997 42 964 


9998 


49.104 


1 


89 


9998 57.290 


9999 


68.750 


9999, 


B5.9401 


^99 


114.58 


1.000 171.88 


1.000 


343.77 





b!) 


60' 


60' 


50' 


50' 


40' 


40' 


30^ 


30' 


20' 20' 


10' 


10' 


b^ 


0) 


cos 1 


cot 


cos 


cot 


cos 


cot 


cos 


cot 


cos cot 


cos 


cot 


4> 

2, 



TABLE VII 
RODS IN FEET, IQTHS AND lOOTHS OF FEET 



O 


Feet 


O 


Feet 


O 


Feet 


^3 
O 


Feet 


o 


Feet 


« 




Pi 




tf 




« 




K 




1 


16.50 


21 


346.50 


41 


676.50 


61 


1006.50 


81 


1336.50 


2 


33.00 


22 


363.00 


42 


693.00 


62 


1023.00 


82 


1353.00 


3 


49.50 


23 


379.50 


43 


709.50 


63 


1039.50 


83 


1369.50 


4 


66.00 


24 


396.00 


44 


726.00 


64 


1056.00 


84 


1386.00 


5 


82.50 


25 


412.50 


45 


742.50 


65 


1072.50 


85 


1402.50 


6 


99.00 


26 


429.00 


46 


759.00 


Q>Q 


1089.00 


86 


1419.00 


7 


115.50 


27 


445.50 


47 


775.50 


61 


1105.50 


87 


1435.50 


8 


132.00 


28 


462.00 


48 


792.00 


68 


1122.00 


88 


1452.00 


9 


148.50 


29 


478.50 


49 


808.50 


69 


1138.50 


89 


1468.50 


10 


165.00 


30 


495.00 


50 


825.00 


70 


1155.00 


90 


1485.00 


11 


181.50 


31 


511.50 


51 


841.50 


71 


1171.50 


91 


1501.50 


12 


198.00 


32 


528.00 


52 


858.00 


72 


1188.00 


92 


1518.00 


13 


214.50 


33 


544.50 


53 


874.50 


73 


1204.50 


93 


1534.50 


14 


231.00 


34 


561.00 


54 


891.00 


74 


1221.00 


94 


1551.00 


15 


247.50 


35 


577.50 


55 


907.50 


75 


1237.50 


95 


1567.50 


16 


264.00 


36 


594.00 


56 


924.00 


76 


1254.00 


96 


1584.00 


17 


280.50 


37 


610.50 


57 


940.50 


77 


1270.50 


97 


1600.50 


18 


297.00 


38 


627.00 


58 


957.00 


78 


1287.00 


98 


1617.00 


19 


313.50 


39 


643.50 


59 


973.50 


79 


1303.50 


99 


1633.50 


20 


330.00 


40 


660.00 


60 


990.00 


80 


1320.00 


100 


1650.00 













TABLE VIII 












LINKS IN FEET, lOTHS AND lOOTHS OF FEET 




w 




m 




w 




w 




rr> 




K 




^ 




^ 




^ 




J£ 




^ 




^ 




C 


Feet 


c 


Feet 


C 


Feet 


C 


Feet 


c 


Feet 


c 


Feet 


'^ 




'^ 




'^ 




3 




"v3 




'^ 




1 


0.66 


18 


11.88 


35 


23.10 


52 


34.32 


69 


45.54 


86 


56.76 


2 


1.32 


19 


12.54 


36 


23.76 


53 


34.98 


70 


46.20 


87 


57.42 


3 


1.98 


20 


13.20 


37 


24.42 


54 


35.64 


71 


46.86 


88 


58.08 


4 


2.64 


21 


13.86 


38 


25.08 


55 


36.30 


72 


47.52 


89 


58.74 


5 


3.30 


22 


14.52 


39 


25.74 


56 


36.96 


73 


48.18 


90 


59.40 


6 


3.96 


23 


15.18 


40 


26.40 


57 


37.62 


74 


48.84 


91 


60.06 


7 


4.62 


24 


15.84 


41 


27.06 


58 


38.28 


75 


49.50 


92 


60.72 


8 


5.28 


25 


16.50 


42 


27.72 


59 


38.94 


76 


50.16 


93 


61.38 


9 


5.94 


26 


17.16 


43 


28.38 


60 


39.60 


77 


50.82 


94 


62.04 


10 


6.60 


27 


17.82 


44 


29,04 


61 


40.26 


78 


51.48 


95 


62.70 


11 


7.26 


28 


18.48 


45 


29.70 


62 


40.92 


79 


52.14 


96 


63.36 


12 


7.92 


29 


19.14 


46 


30.36 


63 


41.58 


80 


52.80 


97 


64.02 


13 


8.58 


30 


19.80 


47 


31.02 


64 


42.24 


81 


53.46 


98 


64.68 


14 


9.24 


31 


20.46 


48 


31.68 


65 


42.90 


82 


54.12 


99 


65.34 


15 


9.90 


32 


21.12 


49 


32.34 


66 


43.56 


83 


54.78 


100 


66.00 


16 


10.56 


33 


21.78 


50 


33.00 


67 


44.22 


84 


55.44 


101 


66.66 


17 


11.22 


34 


22.44 


51 


33.66 


68 


44.88 


85 


56.10 


102 


67.32 



Table IX. TANGENTS 


AND 


EXTERNALS TO A V 


' CURVE 


I 


T 


E 


1=10'' 


I 


T 


£ 


1=20° 


I 


T 


£ 


1=30' 


1° 1 50.00 


.218 


+ 


11* 


551.70 


26.500 


+ 


21° 


1061.9 


97.577 


4- 


10' 


58.34 


.297 


5'»C. 


10' 


560.11 


27.313 


5°C 


10' 


1070.6 


99.155 


20' 


66.67 


.388 


20' 


568.53 


28.137 


20' 


1079.2 


100 . 75 


5°C 


30' 


75.01 


.491 


T 


30' 


576.95 


28.974 


T 


30' 


1087.8 


102.35 


T 


40^ 


83.34 


.606 


,03 


40' 


585.36 


29.824 


.06 


40' 


1096.4 


103.97 


.10 

E 


50' 


91.68 


.733 


E 


50' 


593.79 


30.686 


E 


50' 


1105.1 


105.60 


2° 


100.01 


.873 


.001 


12° 


602.21 


31.561 


.006 


22° 


1113.7 


107.24 


.013 


10' 


108.35 


1.024 




10' 


610.64 


32.447 




10' 


1122.4 


108.90 




20' 


116.68 


1.188 




20' 


619.07 


33.347 




20' 


1131.0 


110.57 




30' 


125.02 
133.36 


1.364 
1.552 




30' 
40' 


627.50 
635 . 93 


34.259 
35.183 




30' 
40' 


1139.7 
1148.4 


112.25 
113.95 




40' 








50' 


141.70 


1.752 




50' 


644.37 


36.120 




50' 


1157.0 


115.66 




30 


150.04 


1.964 


WC. 


130 


652.81 


37.070 


10° C. 


23- 


1165.7 


117,38 


10° C. 


10' 


158.38 


2.188 


T 


10' 


661.25 


38.031 


T 


10' 


1174.4 


119.12 


T 


20' 


166.72 


2.425 


.06 


20' 


669.70 


39.006 


.13 


20' 


1183.1 


120.87 


30' 


175.06 


2.674 


30' 


678.15 


39.993 


30' 


1191.8 


122.63 


.19 


40' 


183.40 


2.934 


E 


40' 


686.60 


40.992 


E 


40' 


1200.5 


124.41 


E 


50' 


191.74 


3.207 


.003 


50' 


695.06 


42.004 


.011 


60' 


1209.2 


126.20 


.025 


4** 


200.08 


3.492 




14° 


703.51 


43.029 




24° 


1217.9 


128.00 




10' 


208.43 
216.77 


3.790 
4.099 




10' 
20' 


711.97 
720.44 


44.066 
45.116 




10' 
20' 


1226.6 
1235.3 


129.82 
131.65 




20' 








30' 


225.12 


4.421 




30' 


728.90 


46.178 




30' 


1244.0 


133.50 




40' 


233.47 


4.755 




40' 


737.37 


47.253 




40' 


1252.8 


135.35 




50' 


241.81 


6.100 


15«C. 


50' 


745.85 


48.341 


16»C. 


60' 


1261.5 


137.23 


16° C. 


5** 


250.16 


6.459 


T 


16° 


754.32 


49.441 


T 


25° 


1270.2 


139.11 


T 


10' 


258.51 


5.829 


.09 


10' 


762.80 


50.554 


.19 


10' 


1279.0 


141.01 


.29 


20' 


266.86 


6.211 


E 


20' 


771.29 


51.679 


E 


20' 


1287.7 


142.93 


E 


30' 


275.21 


6.606 


.004 


30' 


779.77 


52.818 


.017 


30' 


1296.5 


144.85 


.038 


40' 


283.57 


7.013 


40' 


788.26,53.969 


40' 


1305.3 


146.79 


50' 


291.92 


7.432 




50' 


796.75 55.132 




60' 


1314.0 


148.76 




fio 


300.28 
308.64 


7.863 
8.307 




16° 

10' 


805.25 
813.75 


56.309 

57.498 




26° 

10' 


1322.8 
1331.6 


150.71 
152.69 





10' 








20' 


316.99 


8.762 




20' 


822.25 


58.699 




20' 


1340.4 


154.69 




30' 


325.35 


9.230 


20«C. 


30' 


830.76 


59.914 


20«C. 


30' 


1349.2 


156.70 


20° C. 


40' 


333.71 


9.710 


40' 


839.27161.141 


40' 


1358.0 


158.72 


60' 


342.08 


10.202 


T 


50' 


847.78 


62.381 


T 


50' 


1366.8 


160.76 


T 


70 


350.44 


10.707 


.13 

E 


ir 


856.30 


63.634 


27° 


1375.6 


162.81 


.39 
E 


10' 


358.81 


11.224 


10' 


864.82 


64.900 


10' 


1384.4 


164.86 


20' 


367.17 


11.753 


.006 


20' 


873.35 


66.178 


.022 


20' 


1393.2 


166.95 


.051 


30' 


375.54 


12.294 




30' 


881.88 


67.470 




30' 


1402.0 


169.04 




40' 


383.91 


12.847 




40' 


890.41 


68.774 




40' 


1410.9 


171.15 




50' 
8* 


392.28 
400.66 


13.413 
13.991 




50' 
18° 


898.95 
907.49 


70.091 
71.421 




50' 
28° 


1419.7 
1428.6 


173.27 
175.41 










10' 


409.03 


14.682 


26'»C. 


10' 


916.03 


72.764 


26° C. 


10' 


1437.4 


177.65 


25° a 


20' 


417.41 


15.184 


20' 


924.58 


74.119 


20' 


1446.3 


179.72 


30' 


425.79 


15.799 


T 


30' 


933.13 


75.488 


T 


30' 


1455.1 


181.89 


T 


40' 


434.17 


16.426 


.16 


40' 


941.69 


76.869 


.32 


40' 


1464.0 


184.08 


.49 


50' 


442.65 


17.065 


E 


50' 


950.25 


78.264 


E 


50' 


1472.9 


186.29 


E 


y» 


450.93 


17.717 


.007 


19° 


958.81 


79.671 


.028 


29° 


1481.8 


188.61 


.065 


10' 


459.32 


18.381 




10' 


967.38 


81.092 




10' 


1490.7 


190.74 




20' 
30' 
40' 


467.71 
476.10 
484.49 


19.058 

iQ 74.ft 




20' 
30' 
40' 


975.96 
984.53 
993.12 


82.525 
83.972 
85.431 




20' 
30' 
40' 


1499.6 
1508.5 
1517.4 


192.99 
195.26 
197.63 




20.447 








50' 


492.88 


21.161 




50' 


1001.7 


86.904 




50^ 


1526.3 


199.82 




10° 


501.28 


21.887 


30° C. 


20° 


1010.3 


88.389 


30* C. 


30° 


1535.3 


202.12 


30° C. 


10' 


509.68 


22.624 


T 


10' 


1018.9 


89.888 


T 


10' 


1544.2 


204.44 


T 


20' 


518.08 


23.375 


.19 


20' 


1027.5 


91.399 


.39 


20' 


1553.1 


206.77 


.59 


30' 


526.48 


24.138 


E 


30' 


1036.1 


92.924 


E 


30' 


1562.1 


209.12 


E 


40' 


534.89 


24.913 


40' 


1044.7 


94.462 


40' 


1571.0 


211.48 


50' 


543.29 


25.700 


.008 


60' 


1053.3 


96.013 


.034 


50' 


1580.0 


213.86 


.078 



T-R tanHI 



E = R exaeo H I 



Table IX TANGENTS AND EXTERNALS TO A 1^ 


CURVE 


I 


T 


£ 


1=40° 


I 


T 


£ 


1=50° 


I 


T 


£ 


1=60° 


Sl^ 


1589.0 


216.3 


4. 


41^^ 


2142.2 


387.4 


4- 


61° 


2732.9 


618.4 


4. 


i(y 


1598.0 


218.7 


6°C. 


10' 


2151.7 


390.7 


6°C. 


10' 


2743 . 1 


622.8 


5°C. 


20' 


1606.9 


221.1 


20' 


2161.2 


394.1 


20' 


2753.4 


627.2 


30' 


1615.9 


223.5 


T 


30' 


2170.8 


397.4 


T 


30' 


2763.7 


631.7 


T 


40' 


1624.9 


226.0 


.13 


40' 


2180.3 


400.8 


.17 


40' 


2773.9 


636.2 


.21 


60' 


1633.9 


228.4 


E 


60' 


2189.9 


404.2 


E 


60' 


2784.2 


640.7 


E 


32° 


1643.0 


230.9 


.023 


42° 


2199.4 


407.6 


.037 


62* 


2794. 


646.2 


.066 


10' 


1652.0 


233.4 




10' 


2209.0 


411.1 




10' 


2804.9 


649.7 




20 


1661.0 


235.9 




20' 


2218.6 


414.5 




20' 


2815.2 


654.3 




30' 


1670.0 
1679.1 


238.4 
241.0 




30' 
40' 


2228.1 
2237.7 


418.0 
421.4 




30' 
40' 


2825.6 
2835.9 


658.8 
663.4 




40' 








60' 


1688.1 


243.5 




60' 


2247.3 


425.0 




60' 


2846.3 


668.0 




33» 


1697.2 


246.1 


lO'C. 


430 


^57.0 


428.6 


10** C. 


53° 


2856.7 


672.7 


10° C. 


10' 


1706.3 


248.7 


T 


10' 


2266.6 


432.0 


T 


10' 


2867.1 


677.3 


T 


20' 


1715.3 


251.3 


.26 


20' 


2276.2 


435.6 


.34 


20' 


2877.5 


682.0 


.42 


30' 


1724.4 


253.9 


30' 


2285.9 


439.2 


30' 


2888.0 


686.7 


40' 


1733.5 


256.5 


E 


40' 


2296.6 


442.8 


E 


40' 


2898.4 


691.4 


E 


M' 


1742.6 


259.1 


.046 


60 


2305.2 


446.4 


.076 


60' 


2908.9 


696.1 


.112 


34° 


1761.7 


261.8 




440 


2314.9 


450.0 




64° 


2919.4 


700.9 




10' 


1760.8 


264.5 




10' 


2324.6 


453.6 




10' 


2929.9 


705.7 




20' 


1770.0 


267.2 




20' 


2334 . 3 


457.3 




20' 


2940 . 4 


710.6 




30' 


1779.1 


269.9 




30' 


2344 . 1 


461.0 




30' 


2951.0 


715.3 




40' 


1788.2 


272.6 




40' 


2353.8 


464.6 




40' 


2961.5 


720.1 




60' 


1797.4 


276.3 


15«C. 


50' 


2363.5 


468.4 


15<>C. 


50' 


2972.1 


726.0 


15° C. 


35° 


1806.6 


278.1 


T 


45*> 


2373.3 


472.1 


T 


66° 


2982.7 


729.9 


T 


10' 


1815.7 


280.8 


.40 


10' 


2383 . 1 


475.8 


.61 


10' 


2993.3 


734.8 


.63 


20' 


1824.9 


283.6 


E 


20' 


2392.8 


479.6 


E 


20' 


3003.9 


739.7 


E 


30' 


1834.1 


286.4 


.070 


30' 


2402.6 


483.4 


.116 


30' 


3014.6 


744.6 


.168 


40' 


1843.3 


289.2 


40' 


2412.4 


487.2 


40' 


3025.2 


749.6 


60' 


1852.6 


292.0 




50' 


2422.3 


491.0 




60' 


3035.8 


764.6 




36° 

10' 


1861.7 
1870.9 


294.9 
297.7 




4eo 

10' 


2432.1 
2441.9 


494.8 
498.7 




66° 

10' 


3046.6 
3057.2 


7«;q a 








/oy .0 
764.6 




20' 


1880.1 


300.6 




20' 


2451.8 


502.6 




20' 


3067.9 


769.7 




30' 


1889.4 


303.5 


200 c. 


30' 


2461.7 


506.4 


20*^ C. 


30' 


3078.7 


774.7 


20° C. 


40' 


1898.6 


306.4 


40' 


2471.5 


610.3 


40' 


3089.4 


779.8 


60' 


1907.9 


309.3 


T 


50' 


2481.4 


614.3 


T 


60' 


3100.2 


784.9 


T 


37° 


1917.1 


312.2 


.63 
E 


47° 


2491.3 


518.2 


.68 
E 


57° 


3110.9 


790.1 


.84 
E 


10' 


1926.4 


315.2 


10' 


2501.2 


622.2 


10' 


3121.7 


795.2 


20' 


1935.7 


318.1 


.093 


20' 


2511 2 


626.1 


.161 


20' 


3132.6 


800.4 


.226 


30' 


1945.0 


321.1 




30' 


2521 1 


530.1 




30' 


3143.4 


805.6 




40' 


1954.3 


324.1 




40' 


2531.1 


534.2 




40' 


3154.2 


810.9 




60' 
38° 


1963.6 
1972.9 


327.1 
330.2 




50' 
48° 


2541.0 
2551.0 


638.2 
542.2 




60' 
58* 


3165.1 
3176.0 


816.1 
821.4 










10' 


1982.2 


333.2 


26»C. 


10' 


2561.0 


546.3 


25* C. 


10' 


3186.9 


826.7 


26«C. 


20' 


1991.5 


336.3 


20' 


2571.0 


550.4 


20' 


3197.8 


832.0 


30' 


2000.9 


339.3 


T 


30' 


2581.0 


554.5 


T 


30' 


3208.8 


837.3 


T 


40' 


2010.2 


342.4 


.67 


40' 


2591.0 


558.6 


.86 


40' 


3219.7 


842.7 


1.05 


60' 


2019.6 


345.5 


E 


50' 


2601.1 


562.8 


E 


60' 


3230.7 


848.1 


E 


290 


2029.0 


348.6 


.117 


49° 


2611.2 


566.9 


.189 


59° 


3241.7 


853.6 


.283 


10' 


2038.4 


351.8 




10' 


2621.2 


571.1 




10' 


3252.7 


858.9 




20' 


2047.8 


354.9 




20' 


2631.3 


575.3 




20' 


3263.7 


864.3 




30' 
40' 


2057 . 2 
2066.6 


358.1 
361.3 




30' 
40' 


2641.4 
2651.5 


579.5 
583.8 




30' 
40' 


3274.8 
3285.8 


869.8 
875.3 










60' 


2076.0 


364.5 




50' 


2661.6 


588.0 




50' 


3296.9 


880.8 




40° 


2085.4 


367.7 


30«C. 


50° 


2671.8 


592.3 


30«C. 


60° 


3308.0 


886.4 


30«C. 


10' 


2094.9 


371.0 


T 


10' 


2681.9 


596.6 


T 


10' 


3319.1 


892.0 


T 


20' 


2104.3 


374.2 


.80 


20' 


2692.1 


600.9 


1.02 


20' 


3330.3 


897.5 


1.27 


30' 


2113.8 


377.5 


E 


30' 


2702.3 


605.3 


E 


30' 


3341.4 


903.2 


E 


40' 


2123.3 


380.8 


40' 


2712.5 


609.6 


40' 


3352.6 


908.8 


60' 


2132.7 


384.1 


.141 


50' 


2722.7 


614.0 


.227 


50' 


3363.8 


914.6 


.340 



T = R tan 3/^ I 



E =s R exsec }4 I 



Table IX. TANGENTS AND 


EXTERNALS TO A P CURVE 


I 


T 


£ 


1=70' 


I 


T 


£ 


1=80° 


I 


T 


£ 


1=90° 


610 


3375.0 


920.2 


4. 


71° 


4086 . 9 


1308.2 


4. 


81° 


4893.6 


1805.3 


+ 


icy 


3386.3 


925.9 




10' 


4099.5 


1315.6 




10' 


4908.0 


1814.7 


20' 


3397.5 


931.6 


5* C. 


20' 


4112.1 


1322.9 


5° C. 


20' 


4922.5 


1824 . 1 


5°C. 


30' 


3408.8 


937.3 


T 


30' 


4124.8 


1330.3 


T 


30' 


4937.0 


1833.6 


T 


40' 


3420.1 


943.1 


.25 


40' 


4137.4 


1337.7 


.30 


40' 


4951.5 


1843.1 


.36 

E 


5(y 


3431.4 


948.9 


E 


50' 


4150.1 


1345.1 


E 


50' 


4966.1 


1852.6 


62« 


3442.7 


954.8 


.080 


72° 


4162.8 


1352.6 


.110 


82° 


4980.7 


1862.2 


.149 


10' 


3454.1 


960.6 




10' 


4175.6 


1360.1 




10' 


4995.4 


1871.8 




20' 


3465.4 


966.5 




20' 


4188.5 


1367.6 




20' 


5010.0 


1881.5 




30' 


3476.8 


972.4 




30' 


4201.2 


1375.2 




30' 


5024.8 


1891.2 




40' 


3488.3 


978.3 




40' 


4214.0 


1382.8 




40' 


5039.5 


1900.9 




50' 


3499.7 


984.3 




50' 


4226.8 


1390.4 




50' 


5054.3 


1910.7 




^o 


3511.1 


990.2 


lO^C. 


73* 


4239.7 


1398.0 


10° C. 


83° 


5069.2 


1920.5 


10° C. 


10' 


3522.6 


996.2 


T 


10' 


4252.6 


1405.7 


T 


10' 


5084.0 


1930.4 


T 


20' 


3534.1 


1002.3 


.51 


20' 


4265.6 


1413.5 


.61 


20' 


5099.0 


1040.3 


.72 


30' 


3545.6 


1008.3 


30' 


4278.5 


1421.2 


30' 


5113.9 


1950.3 


40' 


3557.2 


1014.4 


E 


40' 


4291.5 


1429.0 


E 


40' 


5128.9 


1960.2 


E 


SC 


3568.7 


1020.5 


.159 


SO' 


4304.6 


1436.8 


.220 


50' 


5143.9 


1970.3 


.299 


M« 


3580.3 


1026.6 




740 


4317.6 


1444.6 




84° 


5159.0 


1980.4 




10' 
20' 


3591.9 
3603.5 


1032.8 
1039.0 




10' 
20' 


4330.7 


1452.5 




10' 
20' 


5174.1 
5189.3 


1990.5 
2000.6 






4343 . 8 


1460.4 






30' 


3615.1 


1045.2 




30' 


4356.9 


1468.4 




30' 


5204.4 


2010.8 




40' 


3626.8 


1051.4 




40' 


4370.1 


1476.4 




40' 


5219.7 


2021 . h 




SO' 


3638.5 


1057.7 


15<>C. 


50' 


4383.3 


1484.4 


15° C. 


50' 


5234.9 


2031.4 


15° C. 


66* 


3650.2 


1063.9 


T 


76« 


4396.5 


1492.4 


T 


85* 


5250.3 


2041.7 


T 


lO' 


3661.9 


1070.2 


.76 


10' 


4409.8 


1500.5 


.91 


10' 


52G5.6 


2052.1 


1.09 


20' 


3673.7 


1076.6 


E 


20' 


4423.1 


1508.6 


E 


20' 


5281.0 


2062.5 


E 


30' 


3685.4 


1082.9 


.240 


30' 


4436.4 


1516.7 


.332 


30' 


5296.4 


2073.0 


.450 


40' 


3697 . 2 


1089.3 


40' 


4449.7 


1524.9 


40' 


5311.9 


2083.5 


50' 


3709.0 


1095.7 




50' 


4463.1 


1533.1 




50' 


5327.4 


2094.1 




ftA* 


3720.9 
3732.7 


1102.2 
1108.6 




76« 

10' 


4476.5 
4489.9 


1541.4 
1549.7 




86° 

10' 


5343.0 
5358.6 


2104 7 




10' 






2115:3 




20' 


3744.6 


1115.1 




20' 


4503.4 


1558.0 




20' 


5374.2 


2126.0 




30' 


3756.5 


1121.7 


20° C. 


30' 


4516.9 


1566.3 


20° C. 


30' 


5389.9 


2136.7 


20° C. 


40' 


3768.5 


1128.2 


40' 


4530.4 


1574.7 


40' 


5405.6 


2147.5 


50' 


3780.4 


1134.8 


T 
1.02 


50' 


4544.0 


1583.1 


T 
1.22 


50' 


5421.4 


2158.4 


T 
1.45 


67*^ 


3792.4 


1141.4 


E 


77* 


4557.6 


1591.6 


E 


87» 


5437.2 


2169.2 


E 


10' 


3804.4 


1148.0 


10' 


4571.2 


1600.1 


10' 


5453 . 1 


2180.2 


20' 


3816.4 


1154.7 


.321 


20' 


4584.8 


1608.6 


.445 


20' 


5469.0 


2191.1 


.603 


30' 


3828.4 


1161.3 1 


30' 


4598.5 


1617.1 




30' 


5484.9 


2202.2 




40' 


3840.5 


1168.1 




40' 


4612.2 


1625.7 




40' 


5500.9 


2213.2 




50' 
68° 


3852.6 
3864.7 


1174 8 
1181.6 




50' 
78° 


4626.0 
4639.8 


1634.4 
1643.0 




50' 
88° 


5517.0 
5533.1 


2224.3 
2235.5 










10' 


3876.8 


1188.4 


25<»C. 


10' 


4653.6 


1051.7 


25° C. 


10' 


5549.2 


2246.7 


25° C. 


20' 


.3889.0 


1195.2 


20' 


4667.4 


1660.6 


20' 


5565.4 


2258.0 


30' 


3^01.2 


1202.0 


T 


30' 


4681.3 


1669.2 


T 


30' 


5581.6 


2269.3 


T 


40' 


39U.4 


1208.9 


1.28 


40' 


4695.2 


1C78.1 


1.53 


40' 


5597.8 


2280.6 


1.83 


50' 


3925.6 


1215.8 


E 


50' 


4709.2 


1686.9 


E 


50' 


5614.2 


2292.0 


E 


^9^ 


3937.9 


1222.7 


.403 


79* 


4723.2 


1695.8 


.558 


89° 


5630.5 


2303.5 


.756 


iO' 


3950.2 


1229.7 




10' 


4737.2 


1704.7 




10' 


5646.9 


2315.0 




20' 


3902. 5 


1236.7 




20' 


4751.2 


1713.7 




20' 


5663.4 


2326.6 




30' 
40' 


3074.8 

aO,S7.2 


1243.7 
1250.8 




30' 

40' 


4765.3 
4779.4 


1722.7 
1731.7 




30' 
40' 


5679 9 


2338.2 
2349.8 








569614 




50' 3999.5 


1257.9 




50' 


4793.6 


1740.8 




50' 


5713.0 


2361.6 




70* 4011.9 


1265.0 


30° C. 


80° 


4807.7 


1749.9 


30^ C. 


90* 


5729.7 


2373.3 


30»a 


10' 4024.4 


1272.1 


T 


10' 


4822.0 


1759.0 


T 


10' 


5746.3 


2385.1 


T 


20' 4036.8 


1279.3 


1.54 


20' 


4836.2 


17G8.2 


1.84 


20' 


5763.1 


2397.0 


2.20 


.^(y 4049.3 


1286.5 


E 


30' 


4850.5 


1777.4 


E 


30' 


5779.9 


2408.9 


E 


40' 1 1061.8 


1293.6 


40' 


4864.8 


1786.7 


40' 


5796.7 


2420.9 


50' 


'4074.4 

1 


1300.9 


.485 


50' 


4879.2 


1796.0 


.671 


50' 


5813.6 


2432.9 


.910 



T = Il tanH I 



E = R cxbcc I J I 



Table IX. TANGENTS AND 


EXTERNALS TO A V 


CURVE 


I 


T 


£ 


1=100° 


I 


T 


^ 


1=110° 


I 


T 


£ 


1=120° 


9V 


5830.5 


2444.9 


+ 


101° 


6950.6 


3278.1 


+ 


111° 


8336.7 


4386.1 


+ 


10' 


5847.5 


2457.1 


10' 


6971.3 


3294.1 


10' 


8362.7 


4407.6 


20' 


5864.6 


2469.3 


6*C. 


20' 


6992.0 


3310.1 


6°C. 


20' 


8388.9 


4429.2 


6°C. 


s(y 


5881.7 


2481.5 


T 


30' 


7012.7 


3326.1 


T 


30' 


8415.1 


4460.9 


T 


40' 


5898.8 


2493.8 


.43 


40' 


7033.6 


3342.3 


.51 


40' 


8441.6 


4472.7 


.62 
E 


50' 


5916.0 


2506.1 


E 


50' 


7064.5 


3358.5 


E 


60' 


8468.0 


4494.6 


920 


5933.2 


2518.5 


.200 


102° 


7075.5 


3374.9 


.268 


112° 


8494.6 


4616.6 


.360 


10' 


5950.5 


2531.0 




10' 


7096.6 


3391.2 




10' 


8521.3 


4538.8 




20' 


5967.9 


2543.5 




20' 


7117.8 


3407.7 




20' 


8548.1 


4561.1 




30' 


5985.3 
6002.7 


2556.0 
2568.6 




30' 
40' 


7139.0 
7160.3 


3424.3 
3440.9 




30' 
40' 


8575.0 
8602.1 


4583.4 
4606.0 




40' 








fiC 


6020.2 


2581.3 




50' 


7181.7 


3457.6 




50' 


8629.3 


4628.6 




98» 


6037.8 


2594.0 


10* C. 


103* 


7203.2 


3474.4 


*10° C. 


113° 


8666.6 


4661.3 


10* C. 


10* 


6055.4 


2606.8 


T 


10' 


7224.7 


3491.3 


T 


10' 


8684.0 


4674.2 


T 


20' 


6073.1 


2619.7 




20' 


7246.3 


3508.2 




20' 


8711.5 


4697.2 


30' 


6090.8 


2632.6 


.86 


30' 


7268.0 


3525.2 


.103 


30' 


8739.2 


4720.3 


1.25 


40' 


6108.6 


2645.6 


E 


40' 


7289.8 


3542.4 


E 


40' 


8767.0 


4743.6 


E 


60' 


6126.4 


2658.5 


.401 


60' 


7311.7 


3559.6 


.636 


60' 


8794.9 


4766.9 


.721 


f4<» 


6144.3 


2671.6 




104° 


7333.6 


3576.8 




114° 


8822.9 


4790.4 




10' 


6162.2 


2684.7 




10' 


7355 6 


3594.2 




10' 


8851.0 


4814.1 




20' 


6180.2 


2697 . 9 




20' 


7377.8 


3611.7 




20' 


8879.3 


4837.8 




30' 


6198.3 


2711.2 




30' 


7399.9 


3629.2 




30' 


8907.7 


4861.7 




40' 


6216,4 


2724.5 




40' 


7422.2 


3646.8 




40' 


8936.3 


4885.7 




60' 


6234.6 


2737.9 


15«C. 


50' 


7444.6 


3664.5 


15° C. 


60' 


8965.0 


4909.9 


16»C. 


95« 


6252.8 


2751.3 


T 


105* 


7467.0 


3682.3 


T 


115° 


8993.8 


4934.1 


T 


10' 


6271.1 


2764.8 


1.30 


10' 


7489.6 


3700.2 


1.56 


10' 


9022.7 


4968.6 


1.93 


20' 


6289.4 


2778.3 


E 


20' 


7512.2 


3718.2 


E 


20' 


9051.7 


4983.1 


E 


30' 


6307.9 


2792.0 


.604 


30' 


7534.9 


3736.2 


.806 


30' 


9080.9 


5007.8 




40' 


6326.3 


2805.6 


40' 


7557.7 


3754.4 


40' 


9110.3 


5032.6 


1.09 


50' 


6344.8 


2819.4 




50' 


7580.5 


3772.6 




50' 


9139.8 


5057.6 




10' 


6363.4 
6382.1 


2833.2 
2847.0 




108* 

10' 


7603.5 
7626.6 


3791.0 
3809.4 




116° 

10' 


9169.4 
9199.1 


5082.7 
5107.9 










20' 


6400.8 


2861.0 




20' 


7649.7 


3827.9 




20' 


9229.0 


5133.3 




30' 


6419.5 


2875.0 


20* C. 


30' 


7672.9 


3846.5 


20° C. 


30' 


9259.0 


5158.8 




40' 


6438.4 


2889.0 


40' 


7696.3 


3865.2 


40' 


9289.2 


5184.5 


20* C. 


60' 


6457.3 


2903.1 


T 


50' 


7719.7 


3884.0 


T 


50' 


9319.5 


5210.3 


T 


970 


6476.2 


2917.3 


1.74 
E 


107° 


7743.2 


3902.9 


2.08 
E 


IIT 


9349.9 


5236.2 


2.52 
E 


10' 


6495.2 


2931.6 


10' 


7766.8 


3921.9 


W 


9380.6 


6262.3 


20' 


6514.3 


2945.9 


.809 


20' 


7790.5 


3940.9 


1.08 


20' 


9411.3 


6288.6 


1.46 


30' 


6533.4 


2960.3 




30' 


7814.3 


3960.1 




30' 


9442 . 2 


5315.0 




40' 


6552.6 


2974.7 




40' 


7838.1 


3979.4 




40' 


9473.2 


5341.5 




50' 


6571.9 


2989 . 2 




50' 


7862 . 1 


3998 . 7 




50' 
118* 


9504.4 
9535.7 


5368.2 
5395.1 




98* 


6591.2 


3003.8 




108° 


7886.2 


4018.2 






10' 


6610.6 


3018.4 


25* C. 


10' 


7910.4 


4037.8 


25° C. 


10' 


9567.2 


5422.1 




20' 


6630.1 


3033.1 


20' 


7934.6 


4057.4 


20' 


9598.9 


5449.2 


25* C. 


30' 


6649.6 


3047.9 


T 


30' 


7959.0 


4077.2 


T 


30' 


9630.7 


5476.5 


T 


40' 


6669.2 


3062.8 


2.18 


40' 


7983.5 


4097.1 


2.61 


40' 


9662.6 


5504.0 


3.16 


50' 


6688.8 


3077.7 


E 


50' 


8008.0 


4117.0 


E 


50' 


9694.7 


5531.7 


E 


W 


6708.6 


3092.7 


1.02 


109* 


8032.7 


4137.1 


1.36 


119° 


9727.0 


5559.4 


1.83 


10' 


6728.4 


3107.7 




10' 


8057.4 


4157.3 




10' 


9759.4 


5587.4 




20' 
30' 
40' 


6748.2 
6768.1 
6788.1 


3122.9 
3138.1 
3153.3 




20' 
30' 
40' 


8082.3 
8107.3 
8132.3 


4177.5 
4197.9 
4218.4 




20' 
30' 
40' 


9792.0 
9824.8 
9857.7 


5615.5 
5643.8 
5672.3 










50' 


6808.2 


3168.7 




50' 


8157.5 


4239.0 




50' 


9890.8 


6700.9 




lOO* 


6828.3 


3184.1 


30° C. 


110* 


8182.8 


4259.7 


30° C. 


120* 


9924.0 


5729.7 


30° C. 


10' 


6848.5 


3199.6 


T 


10' 


8208.2 


4280.6 


T 


10' 


9957.5 


5758.6 


T 


20' 


6868.8 


3215.1 


2.62 


20' 


8233.7 


4301.4 


3.14 


20' 


9991.0 


5787.7 


3.81 


30' 


6889.2 


3230.8 


E 


30' 


8259.3 


4322.4 


E 


30' 


10025.0 


5817.0 


E 


40' 


6909.6 


3246.5 


40' 


8285.0 


4.343.6 


40' 


10059.0 


5846.5 


50' 


6930.1 


3262.3 


1.22 


50' 


8310.8 


4364.8 


1.63 


50' 


10093.0 


5876.1 


2.20 



T = R tan }4 I 



E = II exsec H I 



Table X. 

MIDDLE ORDINATES OF RAILS 
Length of Rail (feet) 



c 


R 


30 1 28 


26 


24 


22 


20 


C 


R 


30 


28 


26 


24 1 22 1 20 


O f 


Feet 


Inch 


Inch 


Inch 


Inch 


Inch 


Inch 


o 


Feet 


Inch 


Inch 


Inch 


Inch 


Inch 


Inch 


0-20 


17189 


.08 


.07 


.06 


.05 


.04 


.03 


8 


716.8 


1.88 


1.64 


1.42 


1.20 


1.01 


.84 


0-40 


8594 


.16 


.14 


.12 


.10 


.08 


.07 


9 


637.3 


2.12 


1.84 


1.60 


1.35 


1.14 


.94 


1-0 


5730 


.24 


.20 


.18 


.15 


.13 


.10 


10 


573.7 


2.36 


2.05 


1.78 


1.50 


1.27 


1.04 


1-20 


4297 


.31 


.27 


.23 


.20 


.17 


.13 


11 


521.7 


2.59 


2.26 


1.95 


1.65 


1.39 


1.15 


1-40 


3438 


.39 


.34 


.29 


.25 


. 21 


.17 


12 


478.3 


3.83 


2.47 


2.15 


1.81 


1.54 


1.26 


2-0 


2865 


.47 


.41 


.35 


.30 


.25 


.20 


13 


441.7 


3.05 


2.66 


2.30 


1.96 


1.66 


1.36 


2-20 


2456 


.55 


.48 


.41 


.35 


.29 


.23 


14 


410.3 


3.30 


2.87 


2.48 


2.10 


1.78 


1.46 


2-40 


2149 


.63 


.55 


.47 


.40 


.33 


.27 


15 


383.1 


3.54 


3.08 


2.68 


2.26 


1.91 


1.57 


3-0 


1910 


.71 


.62 


.53 


.45 


.38 


.31 


16 


359.3 


3.76 


3.28 


2.83 


2.40 


2.04 


1.67 


3-20 


1719 


.78 


.68 


.59 


.50 


.42 


.35 


17 


338.3 


4.00 


3.48 


3.02 


2.57 


2.16 


1.78 


3^0 


1563 


.86 


.75 


.65 


.55 


.46 


.38 


18 


319.6 


4.21 


3.67 


3.18 


2.70 


228 


1.87 


4-0 


1433 


.94 


.82 


.71 


.60 


.50 


.42 


19 


302.9 


4.45 


3.89 


3.36 


2.8612.41 


1.98 


4-20 


1323 


1.02 


.89 


.77 


.65 


.55 


.45 


20 


287.9 


4.70 


4.09 


3.55 


3.002.54 


2.09 


4-iO 


1228 


1.10 


.96 


.83 


.70 


.59 


.48 


22 


262.0 


5.16 


4.44 


3.84 


3.302.80 


2.29 


5 


1146 


1.18 


1.03 


.89 


.75 


.63 


.52 


24 


240.5 


5.64 


4.92 


4.20 


3.59;3.04 


2.50 


6 


955.3 


1.41 


1.23 


1.06 


.90 


.76 


.62 


26 


222.3 


6.07 


5.29 


4.58 


3.883.29 


2.70 


7 


819.0 


1.65 


1.44 


1.24 


ll.05 


.89 


.73 












1 





Table XI. 
SHORT RADIUS CURVES 



R&dins 
Feet 



35 
45 

50 
60 
75 
100 
120 
150 
190 
200 
225 
240 
250 
275 
288 
300 
350 
376 
400 
410 



Chord 
Feet 



10 
10 
15 
15 

15 
20 
20 
20 
25 
25 
25 
25 
25 
25 
50 
50 
50 
50 
50 
50 



Central 
Angle 



16-26 

12-46 

17-16 

14-22 

11-30 

11-30 

9-34 

7-39 

7-32 

7-10 

6-25 

5-58 

5-44 

5-12 

9-58 

9-32 

8-12 

7-40 

7-10 

7-00 



Deflection 
Angle 



8-13 
6-23 
8-38 
7-11 
5-45 
5-45 
4-47 
3-49 
3-46 
3-35 
3-12 
2-59 
2-52 
2-36 
4-59 
4-46 
4-06 
3-50 
3-35 
3-30 



Deflection 
for 1 Foot 



49.3 

38.3 

34.5 

28.8 

23.0 

17.3 

14.3 

11.5 

9.15 

8.6 

1.1 

1.1 

6.9 

6.2 

6.0 

5.7 

4.9 

4.6 

4.3 

4.2 



To find length o£ curve divide angle from P. C. to P. T. by central angle of chord, 
and multiply by lengrth of chord. 



Table XII. 
INCLINED DISTANCE OF 100 FT. REDUCED TO HORIZONTAL 



Slope 


Horizontal 
Distance 


Conection 


Rise 
Per Foot 


Slope 


Horizontal 
Distance 


Correction 


Rise 
Per Foot 


0^00' 


100.000 


0.000 


0.000 


8^00' 


99.027 


0.973 


0.139 


15' 


99.999 


0.001 


0.004 


15' 


98.965 


1.035 


0.143 


30' 


99.996 


0.004 


0.009 


80' 


98.902 


1.098 


0.148 


45' 


99.991 


0.009 


0.013 


45' 


98.836 


L164 


0.152 


1 00 


99.985 


0.015 


0.017 


9 00 


98.769 


1.231 


0.156 


15 


99.976 


0.024 


0.022 


15 


98.700 


L300 


0.161 


30 


99.966 


0.034 


0.026 


30 


98.629 


1.371 


0.165 


45 


99.953 


0.047 


0.031 


45 


98.556 


1.444 


0.169 


2 00 


99.939 


0.061 


0.035 


10 00 


98.481 


1.519 


0.174 


15 


99.923 


0.077 


0.039 


15 


98.404 


1.596 


0.178 


30 


99.905 


0.095 


0.044 


30 


98.325 


1.675 


0.182 


45 


99.885 


0.115 


0.048 


45 


98.245 


1.755 


0.187 


3 00 


99.863 


0.137 


0.053 


11 00 


98.163 


L837 


0.191 


15 


99.839 


0.161 


0.057 


15 


98.079 


1.921 


0.195 


30 


99.813 


0.187 


0.061 


80 


97.992 


2.008 


0.199 


45 


99.786 


0.214 


0.065 


45 


97.905 


2.095 


0.204 


4 00 


99.756 


0.244 


0.070 


12 00 


97.815 


2.185 


0.208 


15 


99.725 


0.275 


0.074 


15 


97.723 


2.277 


0.212 


30 


99.692 


0.308 


0.078 


80 


97.630 


2.370 


0.216 


45 


99.657 


0.343 


0.083 


45 


97.534 


2.466 


0.221 


5 00 


99.619 


0.381 


0.087 


13 00 


97.437 


2.563 


0.225 


15 


99.580 


0.420 


0.092 


15 


97.338 


2.662 


0.229 


30 


99.540 


0.460 


0.096 


30 


97.237 


2.763 


0.233 


45 


99.497 


0.503 


0.100 


45 


97.134 


2.866 


0.238 


6 00 


99.452 


0.548 


0.105 


14 00 


97.030 


2.970 


0.243 


15 


99.406 


0.594 


0.109 


15 


96.923 


3.077 


0.246 


30 


99.357 


0.643 


0.113 


30 


96.815 


3.185 


0.250 


45 


99.307 


0.693 


0.118 


45 


96.705 


3.295 


0.255 


7 00 


99.255 


0.745 


0.122 


15 00 


96.593 


3.407 


0.259 


15 


99.200 


0.800 


0.126 


15 


96.479 


3.521 


0.263 


30 


99.144 


0.856 


0.131 


30 


96.363 


3.637 


0.267 


45 


99.087 


0.913 


0.135 


45 


96.246 


3.754 


0.371 



Table XIII. 
MINUTES IN DECIMALS OF A DEGREE. 



30" 


.00833 


10'30" 


.17500 


20' 30" 


.34167 


30 30" 


.50833 


40' 30" 


.67500 


50' 30" 


.84167 


1 00 


.01667 


11 00 


.18333 


21 00 


.35000 


31 00 


.51667 


41 00 


.68333 


51 00 


.85000 


30 


.02500 


30 


.19167 


30 


.35833 


30 


.52500 


30 


.69167 


30 


.85833 


2 00 


.03333 


12 00 


.20000 


22 00 


.36667 


32 00 


.53333 


42 00 


.70000 


52 00 


.86667 


30 


.04167 


30 


.20833 


30 


.37500 


30 


.54167 


30 


.70833 


30 


.87500 


3 00 


.05000 


13 00 


.21667 


23 00 


.38333 


33 00 


.55000 


43 00 


.71667 


53 00 


.88333 


30 


.05833 


30 


.22500 


30 


.39167 


30 


.55833 


30 


.7250<» 


30 


.89167 


4 00 


.06667 


14 00 


.23333 


24 00 


.40000 


34 00 


.56667 


44 00 


.73333 


54 00 


.90000 


30 


.07500 


30 


.24167 


30 


.40833 


30 


.57500 


30 


.74167 


30 


.90833 


5 00 


.08333 


15 00 


.25000 


25 00 


.41667 


35 00 


.58333 


45 00 


.75000 


55 00 


.91667 


30 


.09167 


30 


.25833 


30 


.42500 


30 


.59167 


30 


.75833 


30 


.92500 


6 00 


.10000 


16 00 


.26667 


26 00 


.43333 


36 00 


.60000 


46 00 


.76667 


56 00 


,93333 


30 


.10833 


30 


.27500 


30 


.44167 


30 


.60833 


30 


.77500 


30 


.94167 


7 00 


.11667 


17 00 


.28333 


27 00 


.45000 


37 00 


.61667 


47 00 


.78333 


57 00 


.95000 


30 


.12500 


30 


.29167 


30 


.45a33 


30 


.62500 


30 


.79167 


30 


.95833 


8 00 


.13333 


18 00 


.30000 


28 00 


.46667 


38 00 


.63333 


48 00 


.80000 


58 00 


.96667 


30 


.14167 


30 


.30833 


30 


.47500 


30 


.64167 


30 


.80833 


30 


.97500 


9 00 


.15000 


19 00 


.31667 


29 00 


.48333 


39 00 


.65000 


49 00 


.81667 


59 00 


.98333 


30 


.15833 


30 


.32500 


30 


.49167 


30 


.65833 


30 


.82500 


30 


.99167 


10 00 !. 16667 


20 00 


.33333 


30 00 


.50000 


40 00 


.66667 


50 00 


.83333 


60 00 


L 00000 




' STA>f£ 



DISTANCES FROM SIDE STAKES FOR CROSS-SECTIONING. 

Slope 1H to l. Roadway of Any Width. 



1 


1 


•1 1 


•2 1 


.3 1 


•* 1 


.5 1 


.6 


.7 1 


.8 


•^ 1 





T" 


000 


15 


0.80 


0.45 


0.60 


0.75 


0.90 


1.05 


1.20 


1.85 


"a 


1 


150 


105 


180 


1.95 


2.10 


2.25 


2.40 


2.55 


2.70 


2.85 


1 


8 


3.00 


3.15 


8.90 


3 45 


3.60 


3 75 


3.90 


4.05 


4.20 


485 


2 


8 


4.50 


465 


4.80 


4.95 


5 10 


5 25 


5 40 


6.55 


5.70 


6.85 


8 


4 


COO 


6 15 


6.30 


6.45 


6.60 


6 75 


6.90 


7.05 


7.20 


7.35 


4 


5 


750 


7.65 


7.80 


7.95 


8.10 


8.25 


8.40 


8.55 


8.70 


8.85 


5 


6 


900 


9 15 


9.30 


9.45 


9.60 


9.75 


9.90 


10.05 


10.20 


1085 


6 


7 


10.50 


10 65 


1080 


10.95 


11.10 


11.25 


11.40 


11 55 


1170 


11.85 


7 


8 


12.00 


12 15 


12.80 


12.45 


12 60 


12.75 


12.90 


1305 


13.20 


18.85 


8 


9 


13 50 


1365 


13 80 


13 95 


14.10 


14.25 


14.40 


14 55 


14.70 


14.85 





10 


15.00 


15 15 


15 30 


15 45 


15.60 


15.75 


15.90 


16.05 


16.20 


16 85 


10 


U 


16 50 


16 6-5 


16 80 


16.95 


17 10 


17.25 


17.40 


17.55 


17.70 


17.85 


11 


12 


18 00 


18 15 


18.30 


18 45 


18 60 


18 75 


18.90 


19.05 


19.20 


19 35 


12 


18 


19 50 


19 6.5 


19.80 


19.95 


20.10 


20.25 


20 40 


20.55 


30.70 


20.86 


13 


14 


21.00 


21 15 


21.80 


21.45 


21 60 


21.75 


21.90 


22 05 


22 20 


22 85 


14 


15 


22 50 


22 65 


22 80 


22 95 


23.10 


23.25 


23.40 


23.55 


23.70 


23.85 


15 


16 


24.00 


24 15 


24 30 


24 45 


24 60 


24.75 


24 90 


25 05 


25.20 


25.85 


16 


17 


25.50 


25 65 


25.80 


25 95 


26.10 


26 25 


26 40 


26.55 


26.70 


26.85 


17 


18 


27.00 


27 15 


27.30 


27 45 


27.60 


27.75 


27.90 


28.05 


28 20 


28.35 


18 


19 


28 50 


28 65 


28 80 


28.95 


29.10 


29.25 


29.40 


29.55 


29.70 


29.85 


19 


ao 


30 00 


30 15 


30.30 


30.45 


30.60 


30.75 


30.90 


31.05 


31.20 


31.85 


20 


21 


31 50 


31 65 


31.80 


31.95 


32 10 


32 2S 


32.40 


32.55 


32 70 


82 85 


21 


•23 


133 00 


ai 15 


33 30 


33 45 


33.60 


33 75 


33.90 


34.05 


34.20 


34.35 


23 


J?3 


34 50 


34 65 


34.80 


34.95 


35.10 


35 2,5 


a>40 


35.55 


35.70 


a5 85 


23 


24 


88 00 


80 15 


36.30 


36 45 


36.60 


36.75 


36.90 


37.05 


87.20 


37.85 


24 


2.5 


37 50 


37. fw 


37 80 


37.9.5 


38.10 


38.2.5 


38.40 


38 55 


38.70 


38.85 


25 


26 


39 to 


39 15 


39 30 


39 45 


39 60 


39 75 


39.90 


40.05 


40.20 


40.35 


26 


27 


40 50 


40 65 


40 80 


40.95 


41.10 


41.25 


41 40 


41.55 


41.70 


41.85 


27 


28 


42 00 


42 15 


42.30 


42.45 


42.60 


42 75 


42.90 


43.05 


43 20 


48.35 


28 


29 


43 50 


43 65 


43.80 


43 95 


44.10 


44 25 


44 40 


44.56 


44.70 


44 85 


29 


8U 


45 00 


45 15 


45.80 


45 45 


45.60 


45.7.5 


45.90 


46.05 


46 20 


46.35 


30 


»1 


46.50 


46.65 


46.80 


46 95 


47.10 


47.25 


47.40 


47.55 


47.70 


47.85 


31 


32 


48 00 


48.15 


48.30 


48 45 


48.60 


48 75 


48.90 


49.05 


49 20 


49.35 


82 


as 


49.50 


49 65 


49.80 


49.95 


50.10 


50.25 


50.40 


50.55 


50 70 


50.85 


83 


84 


51 00 


51.15 


51.:30 


51.45 


51.60 


51.75 


51.90 


62.05 


62.20 


62.86 


84 


35 


52 50 


62.65 


52.80 


52.95 


53.10 


53.25 


53.40 


53.55 


63.70 


53.86 


85 


36 


54 00 


54 15 


54 30 


54 45 


54.60 


54.75 


54.90 


65.05 


65.20 


66.35 


30 


37 


5.5 50 


55 65 


5.5.80 


55.95 


56.10 


56.25 


56.40 


56 55 


56 70 


56.85 


87 


38 


57.00 


.57.15 


57.30 


57 45 


57.60 


57 75 


57.90 


58.05 


58 20 


58 35 


88 


39 


58 50 


58.65 


58 80 


58 95 


59.10 


59 25 


59.40 


59 5.5 


59.70 


59.85 


89 


40 


00 00 


60 15 


6<)30 


60 45 


60 60 


60.75 


60 90 


61.05 


61 20 


61.35 


40 


41 


101.50 


61 65 


61 80 


61 95 


62 10 


62 25 


62.40 


63 55 


62 70 


62.85 


41 


42 


63 00 


6:3.15 


G:):^ 


63 45 


63 60 


68 75 


63 90 


64 05 


64 20 


64.35 


43 


43 


!G4..50 


64 65 


(•»4 80 


64 95 


6.5.10 


65 25 


C5 40 


60.55 


65.70 


65.85 


43 


44 


CI3 00 


66 15 


60 30 


66.45 


66.60 


66 75 


66.90 


G7.05 


67.20 


67.35 


44 


45 


67 50 


67 65 


67 80 


67.95 


68.10 


68.25 


68 40 


68. .55 


68.70 


68.85 


45 


46 


69 00 


69 15 


00 30 


69.45 


69.60 


69.75 


69.90 


70.05 


70.20 


70.35 


46 


47 


70 50 


70 65 


70 80 


70 95 


71.10 


71.25 


71 40 


71.55 


71.70 


71.85 


47 


48 


72 00 


72 15 


72.. 30 


72.45 


72.60 


72.75 


72.90 


73 05 


78.20 


73 35 


4$ 


4V 


73 50 


73 65 


73.80 


73.95 


74.10 


74 25 


74.40 


74.55 


74.70 


74.85 


40 


90 


j 75.00 


75.15 


75.30 


75.45 


75.60 


75.75 


75.90 


70.05 


76.30 


76.35 


5y 



Computed by I* L«Ua<l Locke. 



'10 '-^ 



rv- 



/sjni'^" 



rO 



3^^^ 



7 ^/. 



h, "i' 



"U 



r 






i} 



' /v),' 




3^ 



.-o 



'4^ 



. : i\ 



ly